Abstract
This work aims at investigating the geometry of surfaces corresponding to the geometry of solutions of the vortex filament equation in Euclidean 3-space E3 using the quasi-frame. In particular, we discuss some geometric properties and some characterizations of parameter curves of these surfaces in E3.
Highlights
Publisher’s Note: MDPI stays neutral where κ is the curvature of Φ and B the binormal vector field of the Frenet frame
A quasi-Hasimoto surface is a surface whose parameter curves are equipped with the quasi-frame
The aim of this paper is to study the geometry of quasi-Hasimoto surfaces corresponding to the geometry of solutions of the quasi-vortex filament equation in 3D Euclidean space
Summary
Which is a particular case of the Landau–Lifshitz equation for ferromagnetism [5] It is known as the vortex filament equation (VFE), or the localized induction approximation (LIA), or the binormal Equation (BE). A quasi-Hasimoto surface is a surface whose parameter curves are equipped with the quasi-frame. In 2015, Aydin et al [13] studied surfaces corresponding to solutions of the local induction equation in the pseudo-Galilean space G13.
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